Home
Class 11
MATHS
for any four vectors veca,vecb, vecc and...

for any four vectors `veca,vecb, vecc and vecd` prove that `vecd. (vecaxx(vecbxx(veccxxvecd)))=(vecb.vecd)[veca vecc vecd]`

Text Solution

Verified by Experts

`vecd.(vecaxx(vecbxx (vecc xxvecd)))`
`= vecd.(vecaxx((vecb.vecd)vecc- (vecb.vecc)vecd)))`
`vecd. ((vecb.vecd)(veca xx vecc)- (vecb.vecc)(veca xxvecd))`
`=(vecb.vecd)(vecd.(vecaxxvecc))-(vecb.vecc)(vecd.(veca xx vecd))`
`(vecb.vecd) [vecdvecavecc]`
`(vecb.vecd) [veca vecc vecd]`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise JEE Previous Year (Single Question)|28 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise JEE Previous Year (Multiple Question)|11 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise 2.2|15 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|1255 Videos

  • LIMITS AND DERIVATIVES

    CENGAGE|Exercise Solved Examples And Exercises|288 Videos

Similar Questions

Explore conceptually related problems

For any four vectors veca , vecb , vecc , vecd we have (vecaxxvecb)xx(veccxxvecd)=[veca,vecb,vecd]vecc-[veca,vecb,vecc]vecd=[veca,vecc,vecd]vecb-[vecb,vecc,vecd]veca .

for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc) xx (vecc -veca) = 2 veca.vecb xx vecc .

If vectors, vecb, vcec and vecd are not coplanar, the pove that vector (veca xx vecb) xx (vecc xx vecd) + ( veca xx vecc) xx (vecd xx vecb) + (veca xx vecd) xx (vecb xx vecc) is parallel to veca .

A, B C and D are four points in a plane with position vectors, veca, vecb vecc and vecd respectively, such that (veca-vecd).(vecb-vecc)= (vecb-vecd).(vecc-veca)=0 then point D is the ______ of triangle ABC.

The vectors veca-vecb,vecb-vecc,vecc-veca are

If veca , vecb , vecc and vecd are four non-coplanar unit vectors such that vecd makes equal angles with all the three vectors veca, vecb, vecc then prove that [vecd vecavecb]=[vecd veccvecb]=[vecd veccveca]

Prove that: (vecaxxvecb)xx(veccxxvecd)+(vecaxxvecc)xx(vecd xx vecb)+(vecaxxvecd)xx(vecbxxvecc)=-2[vecb vecc vecd] veca

If veca, vecba and vecc are non- coplanar vecotrs, then prove that |(veca.vecd)(vecbxxvecc)+(vecb.vecd)(veccxxveca)+(vecc.vecd)(vecaxxvecb) is independent of vecd where vecd is a unit vector.

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise 2.3
  1. If veca , vecb , vecc and vecd are four non-coplanar unit vectors such...

    Text Solution

    |

  2. Prove that [veclvecmvecn][vecavecbvecc]=|{:(vecl.veca,vecl.vecb,vecl.v...

    Text Solution

    |

  3. If the volume of a parallelepiped whose adjacent edges are vec a=2...

    Text Solution

    |

  4. If veca=hati+hatj + hatk and vecb = hati - 2 hatj+hatk then find the v...

    Text Solution

    |

  5. If vecx.veca=0vecx.vecb=0 and vecx.vecc=0 for some non zero vector vec...

    Text Solution

    |

  6. If veca=hati+hatj + hatk and vecb = hati - 2 hatj+hatk then find the v...

    Text Solution

    |

  7. If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc...

    Text Solution

    |

  8. If veca= vecP + vecq, vecP xx vecb = vec0 and vecq. vecb =0 then prove...

    Text Solution

    |

  9. prove that (veca.(vecbxxhati))hati+(veca.(vecbxxhatj))hatj+ (veca.(vec...

    Text Solution

    |

  10. for any four vectors veca,vecb, vecc and vecd prove that vecd. (vecax...

    Text Solution

    |

  11. If veca and vecb be two non-collinear unit vectors such that vecaxx(ve...

    Text Solution

    |

  12. show that (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc) if and only if veca a...

    Text Solution

    |

  13. Let veca, vecb and vecc be non-zero vectors such that no two are colli...

    Text Solution

    |

  14. If vec p , vec q , vec r denote vector vec bxx vec c , vec cxx vec a...

    Text Solution

    |

  15. Let veca, vecb , vecc be non -coplanar vectors and let equations veca'...

    Text Solution

    |

  16. Given unit vectors hatm hatn and hatp such that angle between hatm and...

    Text Solution

    |

  17. vec a , vec b ,a n d vec c are three unit vectors and every two are...

    Text Solution

    |

  18. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(2)hatj+b(3)hatk and vecc=c(...

    Text Solution

    |